Unitary Cellular Automata and Convolution Algebras
T. E. Raptis
TL;DR
This paper analyzes Linear Unitary Cellular Automata (LUCA) using a new representation, highlighting symmetries linked to signal theory, coding, and combinatorics, and proposes analog implementations via Linear Transmission Line Networks.
Contribution
It introduces a novel representation for LUCA, explores their symmetries, and suggests practical analog emulators using transmission line networks.
Findings
Identifies key symmetries related to signal and coding theory.
Establishes a new representation for LUCA.
Proposes Linear Transmission Line Networks as emulators.
Abstract
The original local, discrete example of Linear Unitary Cellular Automata (LUCA) is analyzed in terms of a new representation previously introduced in [1] for classical CA. Several important underlying symmetries are reviewed and their tight relationship with both signal and coding theory as well as with combinatorics is underlined. A class of analog implementations in the form of Linear Transmission Line Networks (LTLN) is described as possible emulators of this type of dynamics.
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Taxonomy
TopicsCellular Automata and Applications · Cooperative Communication and Network Coding · DNA and Biological Computing